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Constructing a new chaotic system based on the S̆ilnikov criterion. (English) Zbl 1053.37015
Based on the Šilnikov criterion, the authors construct a new chaotic system of quadratic polynomial ordinary differential equations in three dimensions, which has a single equilibrium point. The authors rigorously prove that this system satisfies all conditions stated in the Šilnikov theorem, which clearly reveals its chaos formation mechanism and implies the existence of Smale horseshoes. Moreover, the authors show that their simulation demonstrated there is a route to chaos through period-doubling bifurcations.

MSC:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)
37D15Morse-Smale systems